It sounds like you probably have allergies. You may be allergic to environmental factors such as dander, pollen, or dust. You may also be coming off of a cold or infection. During the day you are able to clear your nose, however when you are sleeping, you can have a buildup causing it to run in the morning

I could just be that once you are up in the morning and moving your sinuses drain and once everything is out of them then you are fine. If it is a concern for you then you should make an appointment and got in and see you doctor they will be able to tell you.